Spin, charge, and single-particle spectral functions of the one-dimensional quarter filled Holstein model

Abstract

We use a recently developed extension of the weak coupling diagrammatic determinantal quantum Monte Carlo method to investigate the spin, charge and single particle spectral functions of the one-dimensional quarter-filled Holstein model with phonon frequency ω0 = 0.1t. As a function of the dimensionless electron-phonon coupling we observe a transition from a Luttinger to a Luther-Emery liquid with dominant 2k f charge fluctuations. Emphasis is placed on the temperature dependence of the single particle spectral function. At high temperatures and in both phases it is well accounted for within a self-consistent Born approximation. In the low temperature Luttinger liquid phase we observe features which compare favorably with a bosonization approach retaining only forward scattering. In the Luther-Emery phase, the spectral function at low temperatures shows a quasiparticle gap which matches half the spin gap whereas at temperatures above which this quasiparticle gap closes, characteristic features of the Luttinger liquid model are apparent. Our results are based on lattice simulations on chains up to L=20 for two-particle properties and on CDMFT calculations with clusters up to 12 sites for the single-particle spectral function.

Peierls to superfluid crossover in the one-dimensional, quarter-filled Holstein model

“…Very similar results have previously been obtained for ω 0 /t = 0.1 [15]. The nonzero spin gap is confirmed by our results for the dynamical spin structure factor S(q, ω) in figure 4(a) (for ω 0 /t = 0.1) and figure 4(b) (for ω 0 /t = 0.5), which reveal the absence of low-lying spectral weight near q = 0.…”

“…For classical phonons, ω 0 = 0, the Peierls instability leads to long-range 2k F charge order at zero temperature. As discussed above, quantum lattice fluctuations (occurring for ω 0 > 0) can melt this order, and lead to a state with dominant but power-law 2k F charge correlations [15], as confirmed by the cusp at 2k F = π/2 in figure 1(a). The magnitude of the peak at q = 2k F initially decreases and then saturates upon increasing the phonon frequency, signalling competing ordering mechanisms as well as enhanced lattice fluctuations.…”

“…The details of the implementation of this algorithm can be found in [13]. The CTQMC method has previously been applied to the spinless [14] and the spinful Holstein model [15], as well as to a model with nonlocal electron-phonon interaction [16]. Simulations are carried out on one-dimensional lattices of length L using periodic boundary conditions.…”

“…The enhancement of the Drude peak follows directly from the dynamical charge structure factor. Using the continuity equation, the optical conductivity and the dynamical charge structure factor are related via [15] …”

Variational Monte Carlo method for electron-phonon coupled systems

“…There are several numerical methods to tackle the problems of electron-phonon coupled systems such as the exact diagonalization (ED) [4,5], the density matrix renormalization group (DMRG) [6][7][8][9][10][11][12], the quantum Monte Carlo (QMC) method [13][14][15][16][17][18][19][20][21][22][23], the dynamical mean-field theory (DMFT) [24][25][26][27][28][29], and so on. Although the ED provides exact results, it is limited to finite clusters.…”